Question

The resistance, R, of a circuit containing these unknown components is (5x+20)Ω
. A 90-volt potential difference across the circuit produces a current of 2.25 amps.

What is the resistance of the unknown component?

Answer 1

To find the resistance \( R \) of the unknown components, we can use Ohm's Law, which states:

\[
V = I \times R
\]

where:
- \( V \) is the voltage (90 volts),
- \( I \) is the current (2.25 amps),
- \( R \) is the resistance.

We need to find \( R \) in terms of the given expression \( 5x + 20 \).

First, we can rearrange Ohm's Law to solve for \( R \):

\[
R = \frac{V}{I}
\]

Substituting the given values:

\[
R = \frac{90 \, \text{volts}}{2.25 \, \text{amps}} = 40 \, \Omega
\]

Now we equate this to the expression for the resistance given by the unknown components:

\[
5x + 20 = 40
\]

Next, we solve for \( x \):

\[
5x + 20 = 40
\]
\[
5x = 40 - 20
\]
\[
5x = 20
\]
\[
x = \frac{20}{5} = 4
\]

Now that we have \( x = 4 \), we can substitute it back to find the resistance:

\[
R = 5x + 20 = 5(4) + 20 = 20 + 20 = 40 \, \Omega
\]

Thus, the resistance of the unknown component is:

\[
\boxed{40 \, \Omega}
\]